People new to science fiction, black holes, or Star Trek might be confused by the new Star Trek movie. "How can we see Spock's mom in episodes of The Original Series (TOS) if she died on Vulcan?" Explanations that glibly proclaim "time travel" don't really explain what happened.
"Time Travel" using a black hole should not be called time travel at all, but instead alternate universe travel.
When you traverse a hyperbolic orbit around a black hole (and cross the event horizon) you "cease to exist" in the same universe you were in prior to the transit. Current physics says you end up in the "future", but what's the fun in that?
Think about what the word "horizon" means. As you watch something go "over the horizon" it has gone beyond your possible influence. Even if you do go to the future, it is a future that has no connection to the universe you left.
So in the movie we have Nero and Spock leaving their universe (the universe of William Shatner, TOS, The Next Generation (TNG), et al) and entering a new universe. This new universe is Our Universe. A universe with Nokia phones and 236 year old records of the Beastie Boys.
A universe where none of the episodes of The Original Series (TOS) exist.
Not merely don't happen, or haven't happened yet or will happen. Not exist.
This is not "time travel", because it has nothing in common with the previous, pre-transit universe. Nero and Spock have "stepped outside" the light cone (the set of all states reachable at the speed of light) of their universe and entered ours. (see The Large Scale Structure of Space-Time by Hawking et al page 169).
Any and all things you know of Star Trek occured in a different universe. There is no possible event path from this universe (with Bud Classic and dilithium crystal mines in Iowa) to a universe in which any event from the previous TV shows or movies occur.
You should think of TOS, TNG, DSN, V and the excreable Enterprise as just dreams, sort of like Dorothy and Oz.